I'm attempting some questions from Zwiebach - A First Course in String Theory, and have got stuck. I've proved that a function $h'(u)$ is periodic. The question then asks me to show that $h(u)=au+f(u)$ where $a$ is a constant and $f(u)$ a periodic function. I can't see how to do this directly from the periodicity of $h'$. Is this possible, or true?